Venus stands naked except for a heavy necklace and a wide-brimmed, feather-pommelled hat, with her arm raised to hold the branch of a tree whose fruits surely make her at the same time an image of Eve. She's thin, angular and tall, with slender thighs and small breasts - a very different and more edgily erotic vision of the nude than you ever see in Italian art, and a look it's tempting to call "modern". Actually, it is medieval.

When German artists crossed the Alps to Venice in the late 15th century they brought back the Italian Renaissance ideal of the well-proportioned human body. Cranach's contemporary Albrecht Dürer even wrote and published his own researches on human proportion. But German art always kept one foot in the Gothic tradition with its gargoyles and demons and tangled foliage; it never quite left the middle ages. In Gothic art there are plenty of naked bodies but they are bony and thin, long and (to Renaissance eyes) "ill-proportioned". The happy result of this tension in Cranach's painting is that Venus, the ancient Greco-Roman goddess of Love, is suddenly and dangerously depicted as a real woman arousing real desire.

Anyway, that's what I've long felt about this powerful example of the greatness and originality of German art. It seems to me that Germany has the most consistently brilliant art tradition in Europe. Germans have excelled in every era, always with a distinct unease that eradicates the supposed divide between "old masters" and "moderns". Dürer and Cranach, Altdorfer and Grünewald in the Renaissance are as unsettling as Friedrich in the Romantic period, Dix in the 1920s and Richter today. Why, I sometimes wonder, isn't everyone as fascinated by German art as they are by, say, the art of Spain? Oh wait a minute ... now I remember.

The news that one of the most compelling pieces of German art in a British collection actually comes with the unsavoury pedigree of having once been owned, looked at and maybe even fantasised over by Hitler is a sad confirmation of the violence done to German history and culture by Germans in the 20th century. The terrible truth is that for many people not just Cranach but even Schubert and Beethoven will remain comparatively closed books because Germanic culture is tainted by Nazi appropriation. The more deeply historians burrow into the archives, the bigger the problem becomes.

There's an old essay by AJP Taylor on Hitler's table talk in which Taylor says Hitler's cultural pretensions meant nothing - there is no need to blame him on German high culture because in reality he was an ignoramus. This old view doesn't really stand up to the compelling evidence that Hitler knew his Wagner in depth. Even Hitler's biographer Ian Kershaw, who is rightly sceptical of any overly humanising interpretation of the Nazi leader, points out that Hitler decided to aid Franco in the Spanish civil war after attending a performance of Siegfried conducted by Wilhelm Furtwängler.

My dilemma - is it OK that I love a painting Hitler owned? - resembles the issues fans of Wagner have to grapple with. In Larry David's great TV show Curb Your Enthusiasm there's a startling scene when Larry takes revenge on a man who criticises him for humming the Wagner's antisemitic Siegfried Idyll, by hiring an orchestra to play Wagner outside the man's house. Larry's right to despise people who would remove Wagner from the canon. All modern classical music and a great deal of modern art and poetry depends on Wagner's one-man revolution in aesthetics. When you listen to Tristan you have the right to identify with past listeners such as Mahler, and ignore the dead and buried Hitlerian connection.

Similarly, Cranach influenced Marcel Duchamp - who identified with his eroticism - as well as Hitler. Unfortunately there's another issue. How did the painting get into Hitler's collection? Was it seized from a Jewish owner? That now seems highly possible as the painting was sold to the National Gallery on the basis of a false provenance after the war. When its full story is told it may even end up leaving the gallery and being resold abroad ... so I'll enjoy it while I can.